Predictive models of species interactions
## [1] "Run Completed at 2018-03-03 06:48:00"
Absence data
Models
Random Baseline
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior predictive error
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 0
## Unobserved stochastic nodes: 50408
## Total graph size: 206884
##
## Initializing modelAssess Convergence
Species Identity
## sink("models/SpeciesIdentity.jags")
## cat("
## model {
##
## for (x in 1:Nobs){
##
## #observation
## logit(s[x])<-alpha[Bird[x],Plant[x]]
## Yobs[x] ~ dbern(s[x])
##
## }
##
## #Assess Model Fit - Predict remaining data
## for(x in 1:Nnewdata){
##
## #Generate prediction
## logit(snew[x])<-alpha[NewBird[x],NewPlant[x]]
## Ynew_pred[x]~dbern(snew[x])
##
## #Assess fit, proportion of corrected predicted observations
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
##
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #derived posterior predictive error
## fitnew<-sum(Enew[])
## }
## ",fill=TRUE)
##
## sink()## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 30684
## Unobserved stochastic nodes: 19724
## Total graph size: 206884
##
## Initializing modelAssess Convergence
Detectability + Species Identity
## sink("models/SpeciesIdentity_Detect.jags")
## cat("
## model {
##
## #True interaction probability for each bird, plant
## for (i in 1:Birds){
## for(j in 1:Plants){
## for(k in 1:Cameras){
## logit(s[i,j,k])<-alpha[i,j]
## z[i,j,k] ~ dbern(s[i,j,k])
## }
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Detection Process
## p[x]<-detect[Bird[x]] * z[Bird[x],Plant[x],Camera[x]]
##
## #Observation
## Yobs[x] ~ dbern(p[x])
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## pnew[x] <- detect[NewBird[x]] * z[NewBird[x],NewPlant[x],NewCamera[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## #Species level priors
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Logit Intercept
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #OBSERVATION PRIOR
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive error
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 30684
## Unobserved stochastic nodes: 575906
## Total graph size: 825256
##
## Initializing modelAssess Convergence
# Species Identity + Detection + Elevation
## sink("models/SpeciesIdentity_Detect_Elevation.jags")
## cat("
## model {
##
## #Ecological Process Model
## #True State for each bird, plant, camera
## for (i in 1:Birds){
## for(j in 1:Plants){
## for(k in 1:Cameras){
##
## #Occurrence
## logit(psi[i,j,k])<-alpha_occ[i] + beta_occ[i] * elevation[k]
## occ[i,j,k] ~ dbern(psi[i,j,k])
##
## #Interaction
## logit(s[i,j,k])<-alpha[i,j]
##
## #Conditional probability of interaction|occurrence
## rho[i,j,k] <- s[i,j,k] * occ[i,j,k]
##
## z[i,j,k] ~ dbern(rho[i,j,k])
## }
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Observation, conditional on detection and occurrence.
## p[x]<-detect[Bird[x]] * z[Bird[x],Plant[x],Camera[x]]
## Yobs[x] ~ dbern(p[x])
##
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## pnew[x]<-detect[NewBird[x]] * z[NewBird[x],NewPlant[x],NewCamera[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Occurrence model
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## beta_season[x] ~ dnorm(0,0.386)
## beta_int[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Intercept
## #logit prior, then transform for plotting
## alpha[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #Observation group prior
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive check
## fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 30684
## Unobserved stochastic nodes: 1132146
## Total graph size: 1955988
##
## Initializing model
##
## user system elapsed
## 7182.411 24.561 7562.584Assess Convergence
Predicted elevation ranges
Model Comparison
By Species
Detectability
Proportion of predicted observations
Proportion of predicted links
## # A tibble: 4 x 4
## # Groups: Model [4]
## Model Presence Absence p
## <chr> <int> <int> <dbl>
## 1 Random 333075 6925 98.0
## 2 Species 260629 79371 76.7
## 3 Species_Detect 75652 94348 44.5
## 4 Species_Detect_Elevation 124612 215388 36.7## [1] "True presence rate is: 16.5"
Predicted network statistics
Dashed line is the observed network from the time-series.
Predicted betadiversity
Split data into wet (November - May) versus dry season (June - October)
Rewiring: Change in the probability of species interaction
## sink("models/SpeciesIdentity_Detect_Elevation_Beta.jags")
## cat("
## model {
##
## #Ecological Process Model
## #True State for each bird, plant, camera
## for (i in 1:Birds){
## for(j in 1:Plants){
## for(k in 1:Cameras){
##
## #Occurrence
## logit(psi[i,j,k])<-alpha_occ[i] + beta_occ[i] * elevation[k]
## occ[i,j,k] ~ dbern(psi[i,j,k])
##
## #Interaction
## logit(s[i,j,k])<-alpha[i,j] + beta_season[i,j] *Season[k]
##
## #Conditional probability of interaction|occurrence
## rho[i,j,k] <- s[i,j,k] * occ[i,j,k]
## z[i,j,k] ~ dbern(rho[i,j,k])
##
## }
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Observation, conditional on detection and occurrence.
## p[x]<-detect[Bird[x]] * z[Bird[x],Plant[x],Camera[x]]
## Yobs[x] ~ dbern(p[x])
##
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## pnew[x]<-detect[NewBird[x]] * z[NewBird[x],NewPlant[x],NewCamera[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Occurrence model
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Interaction probability
## alpha[i,j] ~ dnorm(0,0.386)
## #Effect of season
## beta_season[i,j] ~ dnorm(0,0.386)
## }
## }
##
## #Observation group prior
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive check
## #fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 30684
## Unobserved stochastic nodes: 1132986
## Total graph size: 1961859
##
## Initializing model
##
## user system elapsed
## 7506.279 37.927 7557.858Assess Convergence
Effect of season on interaction probabilities
Dissimilairty in interactions (Beta_WN from Poisot 2012) Dashed line is the observed network from the time-series.
Note that this is really a measure of dissimilairty in one level (hummimngbirds), as the dissimilarity in plants is fixed by the sampling protocol. While there be a correlation between the species pool and the chosen plant to film, this is filtered by a human placing a camera at that plant, and as such isn’t a true measure of plant dissimiality.
Turnover: Change in the probability of species occurrence
## sink("models/SpeciesIdentity_Detect_Elevation_SeasonOcc.jags")
## cat("
## model {
##
## #Ecological Process Model
## #True State for each bird, plant, camera
## for (i in 1:Birds){
## for(j in 1:Plants){
## for(k in 1:Cameras){
##
## #Occurrence
## logit(psi[i,j,k])<-alpha_occ[i] + beta_occ[i] * elevation[k] + beta_season[i] *Season[k] + beta_int[i] *Season[k] * elevation[k]
## occ[i,j,k] ~ dbern(psi[i,j,k])
##
## #Interaction
## logit(s[i,j,k])<-alpha[i,j]
##
## #Conditional probability of interaction|occurrence
## rho[i,j,k] <- s[i,j,k] * occ[i,j,k]
## z[i,j,k] ~ dbern(rho[i,j,k])
##
## }
## }
## }
##
## #Observation Model
## for (x in 1:Nobs){
##
## #Observation, conditional on detection and occurrence.
## p[x]<-detect[Bird[x]] * z[Bird[x],Plant[x],Camera[x]]
## Yobs[x] ~ dbern(p[x])
##
## }
##
## #Assess Model Fit - Predict remaining data
##
## for(x in 1:Nnewdata){
##
## #Generate prediction
## pnew[x]<-detect[NewBird[x]] * z[NewBird[x],NewPlant[x],NewCamera[x]]
##
## #Predicted observation
## Ynew_pred[x]~dbern(pnew[x])
##
## #Assess fit, proportion of corrected predicted links
## Enew[x]<-abs(Ynew[x]-Ynew_pred[x])
##
## }
##
## #Priors
##
## #Occurrence model
## for(x in 1:Birds){
## alpha_occ[x] ~ dnorm(0,0.386)
## beta_occ[x] ~ dnorm(0,0.386)
## beta_season[x] ~ dnorm(0,0.386)
## beta_int[x] ~ dnorm(0,0.386)
## }
##
## #Observation model
## #Detect priors, logit transformed - Following lunn 2012 p85
## for(x in 1:Birds){
## logit(detect[x])<-dcam[x]
## dcam[x]~dnorm(omega_mu,omega_tau)
## }
##
## #Process Model
## for (i in 1:Birds){
## for (j in 1:Plants){
## #Interaction probability
## alpha[i,j] ~ dnorm(0,0.386)
## #Effect of season
## }
## }
##
## #Observation group prior
## omega_mu ~ dnorm(0,0.386)
## omega_tau ~ dunif(0,10)
##
## #derived posterior predictive check
## #fitnew<-sum(Enew[])
##
## }
## ",fill=TRUE)
##
## sink()## Compiling model graph
## Resolving undeclared variables
## Allocating nodes
## Graph information:
## Observed stochastic nodes: 30684
## Unobserved stochastic nodes: 1132146
## Total graph size: 1966339
##
## Initializing model
##
## user system elapsed
## 7448.018 47.428 7550.844Assess Convergence
Predicted elevation ranges
Effect of season on occurrence probabilities
Dissimilairty in interactions (Beta_WN from Poisot 2012) Dashed line is the observed network from the time-series.
Note that this is really a measure of dissimilairty in one level (hummimngbirds), as the dissimilarity in plants is fixed by the sampling protocol. While there be a correlation between the species pool and the chosen plant to film, this is filtered by a human placing a camera at that plant, and as such isn’t a true measure of plant dissimiality.
Sample interaction
Model overlap
Create a kind of venn diagram on PCA of model similarity based on per link discrepency.
## # A tibble: 16 x 3
## # Groups: Model [4]
## Model mean pair
## <chr> <dbl> <chr>
## 1 Species_Detect_Elevation -0.932 Booted Racket-tail_Stromanthe stromant…
## 2 Species -0.917 Booted Racket-tail_Stromanthe stromant…
## 3 Species_Detect -0.912 Brown Inca_Psammisia aberrans
## 4 Species_Detect_Elevation -0.910 Brown Inca_Psammisia aberrans
## 5 Species_Detect -0.896 Booted Racket-tail_Stromanthe stromant…
## 6 Species_Detect_Elevation -0.885 Violet-tailed Sylph_Begonia longirostr…
## 7 Species -0.872 Brown Inca_Psammisia aberrans
## 8 Species_Detect -0.868 Violet-tailed Sylph_Begonia longirostr…
## 9 Species_Detect -0.854 Violet-tailed Sylph_Drymonia tenuis
## 10 Species_Detect_Elevation -0.845 Violet-tailed Sylph_Kohleria affinis
## 11 Species -0.829 Violet-tailed Sylph_Kohleria affinis
## 12 Species -0.810 Violet-tailed Sylph_Drymonia tenuis
## 13 Random -0.531 Fawn-breasted Brilliant_Columnea cilia…
## 14 Random -0.530 Wedge-billed Hummingbird_Drymonia tenu…
## 15 Random -0.528 Gorgeted Sunangel_Gasteranthus lateral…
## 16 Random -0.525 Booted Racket-tail_Palicourea demissa
Without random model
